Recognition of generalized network matrices

In this thesis, we deal with binet matrices, an extension of network matrices. The main result of this thesis is the following. A rational matrix A of size n×m can be tested for being binet in time O(n6m). If A is binet, our algorithm outputs a nonsingular matrix B and a matrix N such that [B N] is the node-edge incidence matrix of a bidirected graph (of full row rank) and A = B-1N. Furthermore, we provide some results about Camion bases. For a matrix M of size n × m', we present a new characterization of Camion bases of M, whenever M is the node-edge incidence matrix of a connected digraph (with one row removed). Then, a general characterization of Camion bases as well as a recognition procedure which runs in O(n2m') are given. An algorithm which finds a Camion basis is also presented. For totally unimodular matrices, it is proven to run in time O((nm)2) where m = m' – n. The last result concerns specific network matrices. We give a characterization of nonnegative {ε, ρ}-noncorelated network matrices, where ε and ρ are two given row indexes. It also results a polynomial recognition algorithm for these matrices.


Advisor(s):
Liebling, Thomas M.
Fukuda, Komei
Year:
2007
Publisher:
Lausanne, EPFL
Keywords:
Other identifiers:
urn: urn:nbn:ch:bel-epfl-thesis3938-4
Laboratories:


Note: The status of this file is: EPFL only


 Record created 2007-09-03, last modified 2018-05-01

Texte intégral / Full text:
Download fulltext
PDF

Rate this document:

Rate this document:
1
2
3
 
(Not yet reviewed)